Is there a way to change the emission number of a particle system, without affecting the emission number of the mesh it's separated from?
Your solution is really a solution; it's not a workaround.

The reason you can't change one without changing the other is because they are the same particle system, just used in two different places. This is just like when you use the same material in two different places; when you change the color of one, it changes in both places.

Deleting the particle system and making a new one with new settings is one way to "unlink" the two. Another way is to make the second particle system a "single user copy." Do this by clicking the number that's next to the name of the particle system. This will keep all of the original settings, but make it into a separate system so that you can change it's settings without affecting the other one.

I hope that helps!